Washington ? The Supreme Court agreed Monday to decide whether minorities can be given a boost to get into universities, a subject still heatedly contested a quarter-century after the justices first addressed affirmative action in college admissions.

The court will tell universities how much weight, if any, they may assign to an applicant’s race. At stake are race-conscious admissions policies at many public and private colleges, law schools and medical schools.

The only time the Supreme Court considered a college race case, the justices issued a split 1978 ruling that banned racial quotas but gave states little other direction.

Both sides of the affirmative action debate wanted the court to try again.

Justices will consider whether some white applicants to the University of Michigan and its law school were rejected unconstitutionally because of their race, under the Constitution’s guarantee of equal protection for all under the law.

Michigan President Mary Sue Coleman said the outcome “will have a profound impact on our nation’s higher education system and on our race relations broadly. … Now is not the time to turn back the clock.”

“The color of your skin determines so many important things about your life experience :quot; where you live, where you go to work and with whom you work. Race still matters in our society. The ideal of colorblindness does not mean we can or should be blind to that reality,” she said.

Opponents contend that race-conscious policies hurt white college applicants by giving slots to less-qualified minority prospects.

“They’re also unfair to minorities who are stigmatized and held to a demeaningly lower standard,” said Curt Levey, a lawyer with the Washington-based Center for Individual Rights, which is representing white students in the challenge.

Levey said black enrollment initially fell when race considerations were abandoned in public colleges in California, Florida, Texas and Washington state. But he said the numbers are increasing, proof that race does not have to be a factor in admissions in the rest of the country.

The Supreme Court announced separately Monday that it would resurrect another controversial issue: whether states can punish homosexuals for having sex. The court ruled in 1986 that consenting adults have no constitutional right to private homosexual sex. Justices will reconsider that in an appeal filed by two men prosecuted under a Texas law that makes it a crime to engage in same-sex intercourse.

The court will hear arguments in the cases next year, and its decisions will be made public before July, just as some justices may be contemplating announcing retirements from the court.

Only two of the justices who considered the 1978 affirmative action case still sit on the court :quot; Chief Justice William H. Rehnquist and Justice John Paul Stevens. Rehnquist, 78, is considered the most likely retirement prospect. He was not at the court Monday because of leg surgery.